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The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…

Numerical Analysis · Mathematics 2025-06-09 Melanie Kircheis , Daniel Potts

We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…

Optimization and Control · Mathematics 2013-10-03 Tatiana Odzijewicz , Agnieszka B. Malinowska , Delfim F. M. Torres

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative…

Classical Analysis and ODEs · Mathematics 2018-09-05 Xiao-Jun Yang , Feng Gao , J. A. Tenreiro Machado , Dumitru Baleanu

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in…

Statistical Mechanics · Physics 2009-11-07 Govindan Rangarajan , Mingzhou Ding

The fluctuation-dissipation theorem (FDT) is a simple yet powerful consequence of the first-order differential equation governing the dynamics of systems subject simultaneously to dissipative and stochastic forces. The linear learning…

Machine Learning · Computer Science 2021-09-29 Manhyung Han , Jeonghyeok Park , Taewoong Lee , Jung Hoon Han

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…

Classical Analysis and ODEs · Mathematics 2009-11-11 A. M. Mathai , R. K. Saxena , H. J. Haubold

A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…

Numerical Analysis · Mathematics 2016-09-15 Soner Aydinlik , Ahmet Kiris

This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU$(2)$-nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional…

Computational Physics · Physics 2017-12-13 Vishal Vaibhav

In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…

Numerical Analysis · Mathematics 2024-09-16 Lidia Aceto , Fabio Durastante

In our recent paper we have established close relationships between state reduction of a fuzzy recognizer and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those…

Formal Languages and Automata Theory · Computer Science 2011-03-01 Aleksandar Stamenković , Miroslav Ćirić , Jelena Ignjatović

The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…

Dynamical Systems · Mathematics 2022-11-22 Mihai Ivan

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…

Rings and Algebras · Mathematics 2008-10-18 John Michael Nahay

Fuzzy Transform (F-transform) has been introduced as an approximation method which encompasses both classical transforms and approximation methods studied in fuzzy modeling and fuzzy control. It has been proved that, under some conditions,…

Numerical Analysis · Mathematics 2020-11-24 Rafael Aleixo

We consider the unified transform method, also known as the Fokas method, for solving partial differential equations. We adapt and modify the methodology, incorporating new ideas where necessary, in order to apply it to solve a large class…

Analysis of PDEs · Mathematics 2018-08-28 Arran Fernandez , Dumitru Baleanu , Athanassios S. Fokas

This paper has taken into advantage the relationship between Fuzzy Relation Equations (FRE) and Concept Lattices in order to introduce a procedure to reduce a FRE, without losing information. Specifically, attribute reduction theory in…

Artificial Intelligence · Computer Science 2024-10-10 David Lobo , Víctor López-Marchante , Jesús Medina

We consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion of a vortex filament with axial flow immersed in an…

Analysis of PDEs · Mathematics 2012-01-04 Masashi Aiki , Tatsuo Iguchi

In this article, a new concept of LR-type interval-valued intuitionistic fuzzy numbers (LR-type IVIFN) has been introduced. The theory has also been enriched by demonstrating diagrammatic representations of LR-type IVIFNs and establishing…

Optimization and Control · Mathematics 2023-01-19 Manisha Malik , S. K. Gupta , Manuel Arana-Jiménez

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…

Numerical Analysis · Mathematics 2018-03-08 K. Mustapha , K. Furati , O. M. Knio , O. Le Maitre

Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…

Numerical Analysis · Mathematics 2025-12-23 Yang Zhao , Haoyu Lu , Junxiong Jia , Tao Zhou

We solve a weakly singular integral equation by Laplace transformation over a finite interval of R. The equation is transformed into a Cauchy integral equation, whose resolution amounts to solving two Fredholm integral equations of the…

Astrophysics · Physics 2007-05-23 B. Rutily , L. Chevallier